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Full text of "Mathematical And Physical Papers - Iii"

230        ON THE TOTAL  INTENSITY  OF  INTERFERING  LIGHT.
A similar formula holds good for q, whence D2I= limit of
Let now
2?r (#'  x)
-----1_------i. = Q.U)
whence
^ ,           7
dx = -=- du,
A7T
and the limits of u are ultimately  oo aud + o , since a ultimately vanishes.    Hence
..    . f
imit Of J
du
A similar formula holds good for y, and we have, therefore,
if A be the whole area of the aperture or apertures. Now / ought to be equal to A, and, therefore,
D = b\.
CASE II.    Aperture in front of a screen.
The formula for the illumination is given   iu  Airy's Tract, Art. 73.    We have as before,
= limit of jjjjjj*****1 cos j^"^- [^ - & + 2/"J - f]
~ y>dx dy dx'dy'